Codazzi, also known as Il Codagora, was born in Bergamo in about 1604. He left the city probably around 1620 and by 1634 was living in Naples, where he became a pupil of Cosimo Fanzago, also from Bergamo. In Naples he also began to work closely with Domenico Gargiulo, nicknamed Micco Spadaro. The two specialized in very different but complementary genres, with Codazzi painting the architecture and Gargiulo, the figures. In 1635-45 he painted the architectural background for the series Storie romane, commissioned from Aniello Falcone, Giovanni Lanfranco and Gargiulo by the viceroy of Naples.
During the Masaniello revolt of July 1647, Codazzi left Naples and moved to Rome, where he remained until his death. There he began to work with Jan Miel, Michelangelo Cerquozzi and Filippo Lauri, becoming the most famous vedutista of his time. He is best known for his architectural fantasies or capricci, in which buildings that had really existed, often based on the ruins of ancient Rome, are set alongside structures of pure invention. His work was crucial to the development of vedutism in the 18th century, notably by Canaletto and Bernardo Bellotto. He died in Rome in November 1670.